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January  2006, 14(1): 187-202. doi: 10.3934/dcds.2006.14.187

Construction of multidimensional spike-layers

Andrea Malchiodi 1,

1. 

SISSA, via Beirut 2-4, 34014 Trieste, Italy

Received  November 2004 Revised  July 2005 Published  October 2005

We consider positive solutions of the equation $- $ε$^2 $Δ $u + u $=$u^p$ in $\Omega$, where $\Omega \subseteq \R^n$, $p > 1$ and ε is a small positive parameter. Neumann boundary conditions are imposed in general. We prove existence of solutions which concentrate at curves or manifolds in $\overline{\Omega}$ when ε → 0.
Keywords: elliptic problem., concentration phenomena, Spike layer.
Mathematics Subject Classification: Primary: 35J25, 35J20; Secondary: 35B3.
Citation: Andrea Malchiodi. Construction of multidimensional spike-layers. Discrete & Continuous Dynamical Systems, 2006, 14 (1) : 187-202. doi: 10.3934/dcds.2006.14.187
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